# Can we choose polarization vectors freely in any given gauge theory?

When quantizing a gauge theory, we obtain spin-1 particles propagating in space-time. When we want to count the degrees of freedom of the theory or, equivalently, when we are trying to decompose the field operator in a LI basis, we use polarization vectors. My question is, in any given gauge choice, for any given gauge theory, can we choose polarization vectors however we like, as long as they form a basis?

For example, can I choose these?

$$$$\epsilon_0=(1,0,0,0)\\ \epsilon_1=(0,1,0,0) \\ \epsilon_2=(0,0,1,0) \\ \epsilon_3=(0,0,0,1)$$$$

Or any linear combination of those? like choosing $$\epsilon_{\pm}=\frac{1}{\sqrt{2}}\big(\epsilon_0 \pm\epsilon_3\big)$$ which are called the forward and backward polarization vectors. I know probably some choices are smarter than others, but my question is whether we are free to choose whichever basis we want.